Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 12 - Section 12.8 - Exponential and Logarithmic Equations and Problem Solving - Exercise Set: 25



Work Step by Step

$\log_{5}(x+3)-\log_{5}x=2$ Combine $\log_{5}(x+3)-\log_{5}x$ as the $\log$ of a division: $\log_{5}\dfrac{x+3}{x}=2$ Rewrite in exponential form: $5^{2}=\dfrac{x+3}{x}$ $\dfrac{x+3}{x}=25$ Take $x$ to multiply the right side of the equation: $x+3=25x$ Solve for $x$: $x-25x=-3$ $-24x=-3$ $x=\dfrac{-3}{-24}$ $x=\dfrac{1}{8}$
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